The 1d20+10 is his Fort save. The DC is calculated per the standard for supernatural abilities: 10 + ½ HD + controlling_ability_mod. It's customary for a supernatural ability to indicate the ability score that the save DC is based on, but it's nearly always Constitution or Charisma. Undead creatures almost always use Charisma. Decimals/fractions always round down in the 3.5 rules.

Thadie is a 1st-level character with the ancestral ghost template applied. She started from a base Charisma of 15 in life, and the template improves this to 19 yielding a modifier of +4, so her specific calculation is 10 + 0 + 4 = 14.

Vumrot just barely squeaked by on this save.

He hasn't been getting 1d100 checks to avoid needing to save because he doesn't understand Goblin, and therefore he doesn't know from her warning, and doesn't have any ranks in Knowledge (religion) that might afford him a basis to know without being warned, that he can avert his eyes from her in order to lessen his risk of being harmed.

If Gorx, the verb, means to introduce unpredictable and frequently negative results, Gorx the proper noun means this particular goblin, and the euphemism "gorx" to mean the spirits that Gorx summons, then we can create endless grammatically correct sentences.

Produce Flame is how we're going to get out of this pickle. Now that there are only two people engaged in melee with this dragon, the next time it uses a full attack it will almost certainly take me off the board and may even kill me outright.

The alternative is that Vumrot has actually had three full turns since he used his breath weapon and if I remember correctly, that's how many rounds he had to wait before he could use it again. He may try to angle into a better position so he can catch at least two of us in the cone, and if that happens maybe we can try to hit him for free when he moves.

"Every normal man must be tempted, at times, to spit on his hands, hoist the black flag and begin slitting throats." - H.L. Mencken

Or, and we can hope, Vumrot decides that there's a good chance he can kill us all but also a good chance he gonna die and takes a gamble to run deeper in the cave where he can kill us all if we persue using his breath weapon. He leaves himself open to some AoO and we get lucky. Or he escapes and we get to bandage our fallen and try something else. Either way, we going to eat some roasted goats tonight.

The ghost has about a 22-25% chance of damaging your allies, even with their eyes averted from her. It would be higher, but Zathrus is unconscious and therefore isn't in danger of seeing her while she's got her gaze attack active. So I don't have to account for his craptacular Fort save.

She's got a more powerful attack available, but it's even less discriminating because it has a wider area of effect and averting your eyes doesn't help against it.

So yeah, not only is the ghost not of much tactical value, but there's a pretty decent argument that she's more dangerous to your allies than she is to Vumrot. The reality is a little more complicated because Vumrot is REALLY badly injured compared to the members of the party who're still on their feet, but if this encounter were just starting, she'd definitely be doing more harm than good.

Relying on ghosts in combat has its good points, but you really need to know more about who you're calling if you want it to go well. An ancestral ghost usually has two special attacks, and most of the time I select them randomly unless I'm generating the ghost for plot reasons. Out of the six special attacks available, one isn't useful in combat. Three of the remaining attacks cover an area and will affect any living creature in range.

That doesn't make them useless, but it's definitely easier to deploy ghosts or ancestral ghosts if you know what the specific individuals can do and choose appropriately to the circumstances. In this particular fight, the best thing would probably have been to call a ghost with access to both Corrupting Touch and telekinesis, because there's virtually no chance of friendly fire with those abilities, and there are modes of attack with both of them that would bypass Vumrot's armor without allowing him a saving throw.

But I was randomly generating these ghosts on demand, so that wasn't likely to happen. They're persistent once I've generated them (I don't create NPCs or unique monsters without making provisions to reuse them later), but you only have about a 2.8% chance that a random ghost will proc with this specific pair of abilities.

There are roughly 780 1-HD ancestral ghosts associated with the Great Horde. It's a statistical certainty that there are individual spirits who'd fit the bill, but the odds of randomly stumbling across one of them are somewhat less than favorable.

I don't think we even rolled high enough on Knowledge checks to know that there are different kinds of dragons. Witnessing fire damage doing higher-than-expected damage is definitely actionable intelligence, though, so I guess that opens up a conversation about whether the character knows what the player rolled, and also that the character knows the damage tally for the dragon went up by higher than that amount after the successful attack. I think Ed has gone to great lengths to describe any amount of fire damage to the dragon as cause for extreme pain and stress for Vumrot, but the argument could be made that the descriptions of non-fire damage in this combat are really evocative, too.

"Every normal man must be tempted, at times, to spit on his hands, hoist the black flag and begin slitting throats." - H.L. Mencken

Gorx called four fire elementals to get the fire started in this cave. Vumrot killed two of them with his breath weapon, and the other two were badly injured (dropped to less than half their maximum hit points). Per the summary in this post, those four were the only ones around that were going to behave as if dominated. He could have called a pair of 4-HD elementals, but since their brethren are all dead or injured, they'd probably just suggest that he gorx himself right in his gorx-hole if he wants them to enter battle on his behalf.

He probably could call the two injured ones and compel them into battle, but that may not be terribly helpful. If Vumrot breathes on them, they'll probably die.

The undead he's been able to call upon recently are a new addition and are present because of the Great Horde's approach, which is why they are not recorded in the linked post.

Fanax has seen a pile of frozen livestock, and some of the aforesaid livestock have been used in an attempt to smother the fire you built—if this were a fire-based dragon, Vumrot probably would just have come out and taken to the air.

At this point, Vumrot has inflicted cold damage on Yonah (twice), six air elementals (they gabbled wildly about icy breath), four fire elementals, Grimvaalk, and Grimvaalk's wolf. And he tried to inflict cold damage on Fanax.

You also have seen him immediately drop everything and use Zathrus as a chew toy in retaliation for a fire-based attack. Even acknowledging that it was a lot of damage all at once, it was somewhat disproportionate—Yonah and Fanax both had inflicted more damage overall, but Vummie didn't go ham on them.

So overall, I don't think it's a secret that Vumrot really dislikes fire. I'm not going to come out and instruct you guys as to whether your characters have noticed or made a connection between the cold damage, the aversion to fire, and the color scheme, and concluded that Vummie is vulnerable to fire. But I certainly don't think you're stepping across any lines if you decide that this is something your characters would have noticed by now.

I knew it!!!! Below average rolls. Look at those 4 1's!!! On a one-tailed that the dice roller is a bitch ass and rolling low cause it hates us, there's a p=.1 which is significant at a .1 level. Given that I'll take a 10% chance of being wrong, I'm going to say that the dice roller does have it out for us.

Chi-square is 14.8 this time, which passes even the very stringent P = 0.50 (critical value 18.338).

I'm not really good enough at statistics to have a strong opinion about the ideal sample size, except that larger is better. If we combine these two runs, we end up with a total chi-square = 20.6, which still is well below the critical value for P = 0.10 (27.204)

Across this entire run of 200d20, we have a chi-square of 26.2, which is below the critical value of 27.204 needed for P = 0.10. I don't think it'd be satisfactory if you want P = 0.25 or better, but by the standards of tabletop gaming it's pretty damn good, beating most physical dice.